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On systems of null sets

K. Bhaskara Rao, R. Shortt (1999)

Colloquium Mathematicae

The collection of all sets of measure zero for a finitely additive, group-valued measure is studied and characterised from a combinatorial viewpoint.

On the Henstock-Kurzweil integral for Riesz-space-valued functions defined on unbounded intervals

Antonio Boccuto, Beloslav Riečan (2004)

Czechoslovak Mathematical Journal

In this paper we introduce and investigate a Henstock-Kurzweil-type integral for Riesz-space-valued functions defined on (not necessarily bounded) subintervals of the extended real line. We prove some basic properties, among them the fact that our integral contains under suitable hypothesis the generalized Riemann integral and that every simple function which vanishes outside of a set of finite Lebesgue measure is integrable according to our definition, and in this case our integral coincides with...

Optimal integrability of the Jacobian of orientation preserving maps

Andrea Cianchi (1999)

Bollettino dell'Unione Matematica Italiana

Dato un qualsiasi spazio invariante per riordinamenti X Ω su un insieme aperto Ω R n , si determina il più piccolo spazio invariante per riordinamenti Y Ω con la proprietà che se u : Ω R n è una applicazione che mantiene l'orientamento e D u n X Ω , allora det D u appartiene localmente a Y Ω .

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